Analysis Seminar

Due to the nonlinear character of Einstein equations, a sequence of metrics, solutions in vacuum, which oscillate with higher and higher frequency may converge to a solution to Einstein equations coupled to some effective energy momentum tensor. This effect is called backreaction, and has been studied by physicists (Isaacson, Burnett, Green and Wald). It has been conjectured by Burnett, under some definition of the high frequency limit, that the only effective energy momentum tensor that could appear corresponds to a massless Vlasov field, and that reciprocally all solutions to Einstein equations coupled to a massless Vlasov field can be approached by a sequence of solutions to Einstein vacuum equations (with higher and higher frequencies oscillations). I will present a work in collaboration with Jonathan Luk around Burnett conjecture and its reverse.